Question 892804
Let {{{ a }}} = pounds of the 5% cement 
and 8% sand mixture needed
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{{{ .05a }}} = pounds of cement in this mixture
{{{ .08a }}} = pounds of sand in this mixture
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Let {{{ c }}} = pounds of additional sand to be added
Also {{{ 255 }}} pounds of cement are added
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(1) Total pounds of mixture =
{{{ a + c + 255 }}}
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The pounds of cement in final mixture:
(2) {{{ .05a + 255 = .12*( a + c + 255 ) }}}
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The pounds of sand in final mixture:
(3) {{{ .08a + c = .15*( a + c + 255 ) }}}
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This is 2 equations and 2 unknowns, so it
should be solvable. If you don't mind, I'll try  to solve it
so I can check it
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(2) {{{ .05a + 255 = .12a + .12c + 30.6 }}}
(2) {{{ .12a - .05a + .12c = 255 - 30.6 }}}
(2) {{{ .07a + .12c = 224.4 }}}
(2) {{{ 7a + 12c = 22440 }}}
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(3) {{{ .08a + c = .15a + .15c  + 38.25 }}}
(3) {{{ -.07a + .85c = 38.25 }}}
(3) {{{ -7a + 85c = 3825 }}}
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Add (2) and (3)
(3) {{{ -7a + 85c = 3825 }}}
(2) {{{ 7a + 12c = 22440 }}}
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{{{ 97c = 26265 }}}
{{{ c = 270.77 }}}
and
(2) {{{ 7a + 12*270.77 = 22440 }}}
(2) {{{ 7a = 22440 - 3249.24 }}}
(2) {{{ 7a = 19190.76 }}}
(2) {{{ a = 2741.54 }}}
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{{{ .05a = .05*2741.54 }}}
{{{ .05a = 137.077 }}}
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{{{ .08a = .08*2741.54 }}}
{{{ .08a = 219.32 }}}
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137.08 pounds of cement from the mixture
219.32 pounds of sand from the mixture
270.77 pounds of additional sand
are needed to make 12% cement and 15% sand mixture
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check:
(2) {{{ .05a + 255 = .12*( a + c + 255 ) }}}
(2) {{{ 137.08 + 255 = .12*( 2741.54 + 270.77 + 255 ) }}}
(2) {{{ 392.08 = .12*3267.31 }}}
(2) {{{ 392.08 = 392.08 }}}
That's hopeful- you can check the other equation
if you agree with my basic setup that is.
Hope this helps